Spin-Vibrational Relaxation in Cr(V) and V(IV) Tetraphenyl Porphyrin Molecular Spin Qubit Candidates

Qubits are fundamental units of quantum computing and quantum information. Efforts from multiple directions are underway to realize their physical realization. Among these, molecular spin qubits, where the spin states of transition metal complexes encode quantum information, offer unique advantages, such as chemical tunability, scalability, and ease of fabrication. However, vibrational and electronic interactions cause faster spin relaxation in them, leading to reduced coherence times. Here, we present a detailed computational study of two transition metal-based molecular spin qubit candidates, V(O)TPP and Cr(N)TPP (TPP = tetraphenylporphyrin), using density functional theory, multiconfigurational ab initio methods, and spin-vibration coupling models. The ab initio calculated spin-vibrational coupling coefficients for low-frequency modes are applied within a perturbative spin-vibrational relaxation framework to estimate T₁ relaxation times and their anisotropy. The faster T₁ relaxation in Cr(V) is attributed to the low-frequency ligand breathing modes, while the pronounced T₁ anisotropy in V(IV) is reflective of its electronic structure and angular momentum coupling pathways. The model reveals how vibrational and electronic factors govern spin relaxation. The anisotropy in T₁ relaxation is found to arise from specific metal-ligand vibrations that are strongly coupled to certain orbital-specific ligand field states. These insights are hoped to advance the rational design of transition metal-based qubits with improved coherence and relaxation characteristics.